I've taken a number of college-level biology classes but never had the opportunity to take a proper statistical one that assumes an understanding of differential equations. So I've always wondered about the definition of fitness in relation to multigenerational effects.

Wikipedia defines absolute fitness as "the proportional change in the abundance of that genotype over one generation attributable to selection." (The phrase "attributable to selection" has a meaning in population statistics not completely explained in the article but which sounds like a sort of partial derivative.) The key phrase here that surprises me is "over one generation." Does this mean that a gene which for most individuals leads to producing a large number of infertile offspring (rather than a moderate number of fertile offspring) would be by definition very fit? What about a gene that produced a large number of fertile offspring, none of which would be likely to ever actually mate? Or what if these problems usually occurred only two or three generations down the line? Surely such genes would be selected against in the long run. So it seems at first like these mutations ought to be considered to have poor fitness even though Wikipedia's naive definition assigns them high fitness.

A more relevant example is a mutation in a female that, were it present in a male, would make it fitter, or vice-versa. For instance, consider a peacock with impressive tail feathers which otherwise has done nothing to stand out from the crowd. Since this individual has overcome the handicap of heavy plumage, we expect this peacock to be rather strong, but since it is forced to carry this plumage, it's not clear that it has any overall advantage over its competition. (Indeed, since the presence of the handicap is obvious and the compensating strength merely inferred, it seems like the population ought to evolve to reject such mutations, not prefer them.) But the peacock's daughters might inherit these strong genes without inheriting the male-specific hindrance of the heavy tail. This gives a strong peacock with a compensating handicap a long-term advantage in expected number of descendants over an average-strength peacock without said handicap. But this is fundamentally multigenerational.

This is hardly a novel idea, so I wonder if there is more precise terminology used. Can "fitness" be given a precise mathematical definition in population statistics that is somewhat model-agnostic, the way temperature can? If so, is my expectation that variation in "fitness" in this precise sense is the main driver of natural selection correct?

I'm not going to drill down into the whole wikipedia article, right now, but the words "the proportional change in the abundance of that genotype over one generation attributable to selection", as they stand, seem pretty clear to me whether or not they are clearly the right words to use to describe what they ate meant to explain.

The "attributable to selection" seems like it would (amongst other things) deal with the proportionate chances that a father's genetic contribution is of one or other half of the paternal genetic pairing. Assuming nothing in that load creates no change in the container-gamete (compared to sibling gametes with the other load option) then luck plays most/all of the part in the most-likely-to-fertilise measure. The variation of build of the container that makes it faster/more durable and chemically more/less keyed to the egg that it might find is not (SFAIK) a function of the loaded sample. So statistical variation (roughly, as you say, a partial derivative) can up/down the resulting allelle frequency outside of the selectability.

Spoiler:

Note that if ever get to the routine stage that genetic selection is performed by shining a scanner on gametes and only allowing 'approved' loads to go that extra step, that would now be counted as selection-not-luck upon the loadout(s). As are current zygote screenings, where that occurs; as are other tests (emryonic and foetal) where they occur - where that is artificial selection, but nonetheless selection. Performed generationally, the loadout mechanism may develop a skew of what is loaded relating to the standards of fitness (oh Brave New World that has such creatures in it!). But, absent of that, right now it's the current luck of the draw adding an error-bar to the ends-up-as-fit distribution.

With that caveat dealt with, the other part is a direct comparison. One could ask that the frequency of alleles of one generation's offspring be compared to the frequency of that new generation's offspring (the suitability of genes that have survived childhood, mated, born fruit to at least the same stage) or of one generation of adults against the adults that follow (have proved matable, fertilely so, of young that were capable of maturing) or conception-to-conception (having fused, which genetic ancestry will get to the point of fusing again).

Conceivably (NPI!) those three different measures will reveal different results, but only where the curve of fitness is changing rapidly inter-generationally through differently-timed fitness mechanisms, so you're potentially catching the edges of up/down-swing differently on a single gap. With two or more adjacent measures, the choice of where the 'tick/tock' of life's cycle is should smudge away.

Spoiler:

You can even measure post-breeding frequencies against the post-breeding frequencies of the next generation, for creatures with a 'grandparent' support system. How post-menopausal matriarchs shape the next level of post-menopausal matriarchs, in species where this is a thing. And fitness of mules/etc can be measured aganst their separate parentages, albeit you'd have to deliberately span the comparison to start and end before the breeding-age to not discover the inflection point and discern only that mules are highly unlikely to breed true, not what fitness the parental genes must have to make a mule.

Alas, that's a lot more words than I thought I'd tap out. And without even (now) going into the sexual dimorphisms of peacock-tail-genes (was mostly going to go into that as part of the tick/tock choice, if you want to work it out for yourself).

I know what I think that phrase is meant to mean, and inmmy head it seems simple before I neex to try to conversevabout its subtleties in human lamguage. Amd I'm not entirely sure it's written to mean what was intended, as I said. And I'm likely to have mis-said my own words along the way, never mind the horribly ill-edited nature of it. Also, IANABiologist. So it is an armchair-understamding of this subset of the field, at best, maybe coloured more by my (again, amateur) exposure to computational evolutions like Darwinian Poetry.

Perhaps "the abundance of that genotype" should only be tallied over those individuals that are still members of the species?Mules and others no longer capable of breeding with the original population are discounted.That doesn't catch the long term problems, but that's a case of 'currently very fit, but declining'.

In terms of the temperature metaphor I think it works. What I believe you and I are thinking of when we say 'fitness' is simply more long-term. A trait could be "hot" right now for creating the next generation, but unless it is "flammable with a decent energy density", it'll become "cold" soon.

Being a dead end path doesn't change the fact that siring a thousand mules will generate a huge increase in your genetic biomass next year and whatever you did to get selected for that is very hot

Any tracking over multiple generations has to take into account the changing environment the genes find themselves in, which greatly complicates the idea of a stable "fitness" score you can assign cross-generationally. So it's not unreasonable to take the simple route and classify it in a single generation; yeah, that super-fertile-but-next-generation-is-infertile gene is *extremely* fit in one generation, but extremely unfit in the next.

(The gene itself couldn't be responsible for the change, after all; it stayed the same in both generations. Clearly there's some second-order effect in gene interactions that's causing the children to be infertile, which counts as a "change in environment" if you're being sufficiently technical.)

SuicideJunkie wrote:Perhaps "the abundance of that genotype" should only be tallied over those individuals that are still members of the species?Mules and others no longer capable of breeding with the original population are discounted.That doesn't catch the long term problems, but that's a case of 'currently very fit, but declining'.

But tallied when? Like, the next generation, or fifty years later? It's not terribly mathematically precise here. Mules aren't a serious problem in any case. The real issue is a trait that will confer different fitness at different generations, not hybridization.

Xanthir wrote:Any tracking over multiple generations has to take into account the changing environment the genes find themselves in, which greatly complicates the idea of a stable "fitness" score you can assign cross-generationally. So it's not unreasonable to take the simple route and classify it in a single generation; yeah, that super-fertile-but-next-generation-is-infertile gene is *extremely* fit in one generation, but extremely unfit in the next.

(The gene itself couldn't be responsible for the change, after all; it stayed the same in both generations. Clearly there's some second-order effect in gene interactions that's causing the children to be infertile, which counts as a "change in environment" if you're being sufficiently technical.)

A change in the chemical environment of the gene perhaps, but not necessarily a change in the environment of the organism or the population.

Anyway, I was hoping there was a more rigorous approach possible, something that captures the idea of a trait that is likely to succeed over time in the population due to selection.

There's that happened with with North American cat species having selection pressure for larger body size because it's better competition for mates while pressing them to an unsustainable size to actually live on the available prey species - long enough term to certainly seem like an advantage. I kinda think you'd have to decide a cutoff at a number of generations. One seems awfully short, though, since I think you'd lose any interactions that involve more than the two involved - not good for humans, orcas, and elephants with "good grandparent" genes....

So much depends upon a red wheel barrow (>= XXII) but it is not going to be installed.

SuicideJunkie wrote:Perhaps "the abundance of that genotype" should only be tallied over those individuals that are still members of the species?Mules and others no longer capable of breeding with the original population are discounted.That doesn't catch the long term problems, but that's a case of 'currently very fit, but declining'.

But tallied when? Like, the next generation, or fifty years later? It's not terribly mathematically precise here. Mules aren't a serious problem in any case. The real issue is a trait that will confer different fitness at different generations, not hybridization.

...

Anyway, I was hoping there was a more rigorous approach possible, something that captures the idea of a trait that is likely to succeed over time in the population due to selection.

Tallied for the next generation since to be fair, you need to scale things relative to the genetic effects instead of random astronomical phenomena.

You could perhaps define a series of scores; FitnessN, for the relative change in abundance N generations later. Determining a value for Fitness∞ won't happen however. In some cases, it may appear to rapidly approach a limit, and you could make educated guesses, but you can't measure it until it has happened and become trivial, and the environment isn't static for projections.

Copper Bezel wrote:One seems awfully short, though, since I think you'd lose any interactions that involve more than the two involved - not good for humans, orcas, and elephants with "good grandparent" genes....

I gave a way that you could deal with that, in a one-generation span of comparison.